How to make a F-curve with a constant and linear part?
Here are a few ways I can think of.

3 Keyframes, linear interpolation.

Simple driver expression   frame if (frame > 100) else 0

Or if you are using modifiers, add two generators and restrict the frame range
0 + 0x for frames 0 to 100
-100 + 1x for frames 100 to 



Also, as suggested here How to change the inherited F-curve independently from the original one ? 
,  I recommend you look at the NLA editor, especially for offsetting the start of actions.